In a fiber optic time domain reflectometer (FOTDR), a pulse of light is launched into one end of a fiber under test at time t=0 and the optical power level leaving the test fiber by way of the same end after a delay T is detected using a photodetector. This power level is representative of the condition of the fiber at a distance vT/2 from the light source and the photodetector (where v is the velocity of light in the fiber). The operations of launching a pulse into the fiber and detecting the optical power level leaving the fiber are repeated for a large number of different delay values, and the resulting data is used to form a display that represents fiber condition as a function of distance.
Conventional FOTDR's use laser diodes to generate the desired light pulses. The range of an FOTDR depends on the amount of energy that is launched into the fiber. The laser diodes of conventional FOTDR's are operated at maximum power level, and therefore in order to increase the range of an FOTDR it is necessary to increase the time for which the laser diode is energized. However, if one simply increases the duration of the light pulse, the resolution of the FOTDR is reduced. Therefore, it has been proposed that a sequence of light pulses should be launched into the fiber and that the power level at which light leaves the fiber should be correlated with that sequence. This technique contemplates applying an electrical signal comprising a sequence of pulses, each of which may be 1 (on) or 0 (off), to the laser diode and thereby launching a corresponding sequence of light pulses into the fiber, and generating a display of the condition of the fiber as a function of distance by correlating a delayed replica of the electrical signal with the output signal of the photodetector, which represents the optical power level leaving the fiber. In P. Healey, "Optical Orthogonal Pulse Compression Codes by Hopping", Electron. Lett., 1981, vol. 17, p. 970, it is reported that the electrical signal can be encoded in accordance with maximal length sequences (M-sequences), and that the optical power level leaving the fiber can be correlated with the delayed replica of the electrical signal using a special technique which yields a correlation function that is zero for all values of relative delay (the difference between the delay suffered due to propagation through the fiber and the delay imposed on the replica of the electrical signal) except zero, and for zero relative delay is dependent on the number of terms in the sequence. Thus, if there is a discontinuity in the fiber at distance v.tau..sub.o /2, giving rise to a reflection that is received at time .tau..sub.o after launching energy into the fiber, and a delayed replica of the electrical signal is correlated with the power level at which light leaves the fiber, the correlation function will be zero for values of delay other than .tau..sub.o. The resolution of the measurement is limited by the duration of each pulse in the sequence rather than by the duration of the sequence. However, the technique described by Healey is subject to the disadvantage that it requires that N sequences of light pulses be transmitted into the fiber and that the power level leaving the fiber be correlated twice for each of the transmitted sequences, where N is the number of elements in the M-sequence.
M. J. E. Golay "Complementary Series" IRE Trans. on Information Theory, 1961, IT-7, p. 82, describes the properties of certain sequences. Golay uses the term "series" to describe what is commonly known as a sequence and therefore the latter term will be used in this specification. The sequences referred to by Golay as complementary series will be referred to in this specification as Golay complementary sequences. A set of Golay complementary sequences may be defined as a pair of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any given separation in one sequence is equal to the number of pairs of unlike elements with the same separation in the other sequence. Golay discusses the application of the properties of Golay complementary sequences to multislit spectrometry, and points out that the use in a multislit spectrometer of slits that are open or closed in accordance with whether the corresponding elements of a group of Golay complementary sequences are of one kind or the other yields improved signal to noise ratio and resolution.
For the general case, Golay assigns values of 1 and 0 to the two kinds of elements of Golay complementary sequences, although he points out that if values of +1 and -1 are assigned then the sum of the autocorrelation functions of the two Golay complementary sequences has zero sidelobes. Thus, if two Golay complementary sequences having elements +1 and -1 are designated by a and b respectively, and the autocorrelation functions for the sequences a and b are designated by c.sub.j and d.sub.j respectively, where j indicates the separation of the sequences that are correlated, then EQU c.sub.j +d.sub.j =0 j.noteq.0 (1) EQU c.sub.o +d.sub.o =2n (2)
Healey apparently recognized the possibility and advantage of using Golay complementary sequences where positive and negative values are available for the two kinds of elements of the sequences, but believed that the properties of Golay complementary sequences could not be used when only non-negative values are available.